Algorithm for multiplex network generation with shared links

Multiplex networks have been used to describe multilevel system by the way of combining several layers of sub-networks with one layer representing one sub-level system. Many multiplexes are characterized by a significant shared links in different layers. For this new network framework, research efforts have been paid on the study of its topological and dynamical properties. However, in these studies the network structures are mostly simple or specific, and the shared links in different layers has been mostly neglected, despite the fact that it is an ubiquitous phenomenon in most multiplexes. To systemically study multiplex network, a general multiplex network framework is necessary. In this work, we introduce an algorithm to generate a multiplex networks with shared links whose degree correlation functions of all its layers, the nodal degree correlation function between the layers, and the size of the resulting network are all tunable. Moreover, we give an upper bound of the average degree of the resulting network when the degree correlation functions introduced above are given and make efforts to maximize the average nodal degree of the multiplex networks. This algorithm may serve as a good candidate of standard technique for multiplex network generation.